B Heat transfer in water

Looking back to heat transfer by convection, which means denser molecules move down, lighter molecules move up.
And then water at 4°C expands when cooled further, and at 0°C it contracts when heated. So if water at 0°C in a container is heated from the bottom, its molecules should contract(becomes denser) and should sit well at the bottom but how then is heat transfered to the top?
If we say by conduction, isn't the time to heat such water be much longer since water is a poor conductor of heat.

Molecules don't have a density. The space between them will change as the temperature changes so the Bulk Material density changes. You are suffering here because of the way the phenomenon is being presented. Modern teaching likes to dive into the microscopic world of Particles as soon as possible. If you just consider Convection as a Macroscopic process then you have a better chance of overall understanding. Of course, particles are involved but they don't always need to be brought into the explanation. Dense Water sinks and less dense Water is displaced and rises to the top.

So if water at 0°C in a container is heated from the bottom, its molecules should contract(becomes denser) and should sit well at the bottom but how then is heat transfered to the top?

A very good question. The water on the bottom needs to heat up past the temperature of maximum density before convection starts. The anomalous expansion of water is thought to be the reason that aquatic life survives in very cold conditions. The liquid water under ice is cold but still floats on top of the less cold water beneath. That inhibits convection which, otherwise would take heat from the bottom of the pond and it would all freeze much quicker than it does, just by conduction (as you say, a very slow process for a substance like water).
Weren't we lucky? But for this protection of pond life from freezing to death, we might never have evolved into the splendid PF members you see today.

Molecules don't have a density. The space between them will change as the temperature changes so the Bulk Material density changes. You are suffering here because of the way the phenomenon is being presented. Modern teaching likes to dive into the microscopic world of Particles as soon as possible. If you just consider Convection as a Macroscopic process then you have a better chance of overall understanding. Of course, particles are involved but they don't always need to be brought into the explanation. Dense Water sinks and less dense Water is displaced and rises to the top.

A very good question. The water on the bottom needs to heat up past the temperature of maximum density before convection starts. The anomalous expansion of water is thought to be the reason that aquatic life survives in very cold conditions. The liquid water under ice is cold but still floats on top of the less cold water beneath. That inhibits convection which, otherwise would take heat from the bottom of the pond and it would all freeze much quicker than it does, just by conduction (as you say, a very slow process for a substance like water).
Weren't we lucky? But for this protection of pond life from freezing to death, we might never have evolved into the splendid PF members you see today.